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consider the quadratic function f(x)=x^2−5x−6.

determine the following: (enter all numerical answers as integers, fractions, or decimals):

the smallest x-intercept is x= .

the largest x-intercept is x= .

the y-intercept is y= .

the vertex is ( , ).

the line of symmetry has the equation

Part 1) The smallest x-intercept is x=-1

Part 2) The largest x-intercept is x=6

Part 3) The y-intercept is y=-6

Part 4) The vertex is the point (2.5,-12.25)

Part 5) The equation of the line of symmetry is x=2.5

Step-by-step explanation:

we have

step 1

Find the x-intercepts

we know that

The x-intercept is the value of x when the value of the function is equal to zero

so

equate the function to zero

The formula to solve a quadratic equation of the form is equal to

in this problem we have

so

substitute in the formula

therefore

The x-intercepts are

x=-1 and x=6

The smallest x-intercept is x=-1

The largest x-intercept is x=6

step 2

Find the y-intercept

we know that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

therefore

The y-intercept is y=-6

step 3

Find the vertex

we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex

Convert the function into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square, Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

The vertex is the point (2.5,-12.25)

step 4

Find the equation of the line of symmetry

we know that

In a vertical parabola the equation of the line of symmetry is equal to the x-coordinate of the vertex

we have

vertex (2.5,-12.25)

The x-coordinate of the vertex is 2.5

therefore

The equation of the line of symmetry is x=2.5

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step-by-step explanation:

don't report but were is the digram

step-by-step explanation: